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Study of Roseman moves using quandle theory and immersion theory

Research Project

Project/Area Number 26400082
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionTokyo Gakugei University

Principal Investigator

Tanaka Kokoro  東京学芸大学, 教育学部, 准教授 (70448950)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords位相幾何 / 曲面結び目 / ローズマン変形 / カンドル / はめ込み / トポロジー
Outline of Final Research Achievements

We studied independence of Roseman moves for surface-knot diagrams. Firstly, using immersion theory, we shed light on independence of Roseman moves including branch points. More pricisely, we constructed a pair of two 2-knots such that any sequence of Roseman moves between them contains branch points. Secondly, using quandle theory, we shed light on independence of Roseman moves including triple points. More pricisely, we constructed a pair of two 2-knots such that any sequence of Roseman moves between them contains triple points.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Acknowledgement Compliant: 6 results) Presentation (10 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results) Remarks (1 results)

  • [Journal Article] Regular-equivalence of $2$-knot diagrams and sphere eversions2016

    • Author(s)
      Masamichi Takase, Kokoro Tanaka
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: 161 (No. 2) Issue: 2 Pages: 237-246

    • DOI

      10.1017/s0305004116000244

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Independence of Roseman moves including triple points2016

    • Author(s)
      Kengo Kawamura, Kanako Oshiro, Kokoro Tanaka
    • Journal Title

      Algebraic & Geometric Topology

      Volume: 16 (No. 4) Issue: 4 Pages: 2443-2458

    • DOI

      10.2140/agt.2016.16.2443

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Charts, signatures, and stabilizations of Lefschetz fibrations2015

    • Author(s)
      Hisaaki Endo, Seiichi Kamada, Isao Hasegawa, Kokoro Tanaka
    • Journal Title

      Geometry & Topology Monographs

      Volume: 19

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A note on the local relations in geometric formalism of Khovanov homology theory2015

    • Author(s)
      Kokoro Tanaka
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 25 Issue: 01 Pages: 1620001-1620001

    • DOI

      10.1142/s0218216516200017

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On rack colorings for surface-knot diagrams without branch points2015

    • Author(s)
      Oshiro Kanako, Kokoro Tanaka
    • Journal Title

      Topology and its Applications

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The shadow nature of positive and twisted quandle cocycle invariants of knots2015

    • Author(s)
      Seiichi Kamada, Victoria Lebed, Kokoro Tanaka
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] バイカンドル彩色について2016

    • Author(s)
      Kokoro Tanaka
    • Organizer
      研究集会「2016年度琉球結び目セミナー」
    • Place of Presentation
      那覇市伝統工芸館会議室(沖縄県・那覇市)
    • Year and Date
      2016-12-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] The canonical genus of Whitehead doubles of non-prime alternating knots2016

    • Author(s)
      Kokoro Tanaka
    • Organizer
      KOOK-TAPU Workshop of Knots in Tsushima Island
    • Place of Presentation
      TIARA [下対馬離島開発センター] (長崎県・対馬市)
    • Year and Date
      2016-09-06
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Coherent regions of special diagrams of a knot2016

    • Author(s)
      Kokoro Tanaka
    • Organizer
      研究集会「拡大KOOKセミナー2016」
    • Place of Presentation
      大阪電気通信大学(大阪府・寝屋川市)
    • Year and Date
      2016-08-22
    • Related Report
      2016 Annual Research Report
  • [Presentation] 有向結び目図式の非同調領域数の評価について2016

    • Author(s)
      Kokoro Tanaka
    • Organizer
      2016 琉球結び目セミナー
    • Place of Presentation
      那覇市伝統工芸館会議室(那覇市ぶんかテンブス館2階)
    • Year and Date
      2016-02-20
    • Related Report
      2015 Research-status Report
  • [Presentation] Independence of Roseman moves for surface-knot diagrams2016

    • Author(s)
      Kokoro Tanaka
    • Organizer
      東大数理トポロジー火曜セミナー
    • Place of Presentation
      東京大学数理科学研究科(東京都・目黒区)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] The canonical genus of Whitehead doubles of non-prime alternating knots2015

    • Author(s)
      Kokoro Tanaka
    • Organizer
      Knots in Washington XLI
    • Place of Presentation
      George Washington University, Washington DC, USA
    • Year and Date
      2015-12-04
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Roseman変形の独立性について2015

    • Author(s)
      Kokoro Tanaka
    • Organizer
      東京女子大学トポロジーセミナー
    • Place of Presentation
      東京女子大学
    • Year and Date
      2015-11-28
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 多重共役カンドルのホモロジーについて2014

    • Author(s)
      Scott Carter, Atsushi Ishii, Masahico Saito, Kokoro Tanaka
    • Organizer
      ハンドル体結び目とその周辺VII
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2014-10-04 – 2014-10-05
    • Related Report
      2014 Research-status Report
  • [Presentation] Regular-equivalence of 2-knot diagrams and sphere eversions2014

    • Author(s)
      Masamichi Takase, Kokoro Tanaka
    • Organizer
      A Satellite Conference of Seoul ICM 2014: Knots and Low Dimensional Manifolds
    • Place of Presentation
      BEXCO Convention & Exhibition Center II, Busan, Korea
    • Year and Date
      2014-08-22 – 2014-08-26
    • Related Report
      2014 Research-status Report
  • [Presentation] On n-almost positive adequate links2014

    • Author(s)
      Kokoro Tanaka
    • Organizer
      2014 琉球結び目セミナー
    • Place of Presentation
      那覇市ぶんかテンブス館2階 那覇市伝統工芸館会議室
    • Year and Date
      2014-06-21 – 2014-06-22
    • Related Report
      2014 Research-status Report
  • [Remarks] 東京学芸大学 田中心 個人ホームページ

    • URL

      http://www.u-gakugei.ac.jp/~kotanaka/

    • Related Report
      2016 Annual Research Report 2015 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

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